In this piece of work were tested 7 Hydrophobic-Polar sequences in two types of 2D-square space lattices, homogeneous and correlated, the latter simulating molecular crowding included as a geometric boundary restriction. The optimization of the 2D structures was carried out using a variant of Dill's model, inspired by the convex function, which takes into account both the hydrophobic (Dill’s model) and polar interactions, aimed to include more structural information to reach better folding solutions. While using correlated networks, the degrees of freedom in the folding of sequences were limited, and as a result in all cases more successful structural trials were found in comparison to the homogeneous lattice. In particular, the S5 sequence turned out to be the most difficult sequence of the seven folded, this perhaps due to the intrinsic i) degrees of freedom and ii) motifs of the expected 2D HP structure. Regarding S2 and S6 sequences, although optimal folding was not achieved for neither of the two approaches, folding with correlated network approach not only produced better results than homogeneous space, but for both sequences the best values found with crowding were very close to the expected optimal fitness. The sequences S1-S4 and S6 were better folded with medium lattice units for the correlated media, instead, S5 and S7 were better folded with a bit larger degree of lattice unit, revealing that depending on the degrees of freedom and particular folding motifs in each sequence would require particular crowding to achieve better folding. Finally, we claim that in all folded sequences in crowded spaces achieve better results than homogeneous ones.